Center of pressure discussion...

[flyTotheSky]

As we all know the CP moves along the chordline when the AOA changes. As the AOA increases, the CP moves forward and vice versa.

My question is what are the true physics behind this and second, does Newton have anything to say about this phenomona?

 

[meritflyer]

tgrayson or fish would be the person on this one.

 

[seagull]

I'm too tired to write much right now, and tgrayson is probably going to be more patient with the answer, but I will say this: Don't think that Newton is some different explanation of lift. Newtons laws apply, but the are not an alternative to Bernoulli. Rather, Bernoulli is really based on Newton in the first place. The whole notion that somehow a certain weight of air is moved downwards so the wing moves up in an application of Newton's 3rd law is, frankly, a true misunderstanding of what is happening, Newtons laws, and the concept of cause and effect. There are a lot of threads you can search in the tech section on this topic, and tgrayson will do a nice job with it too, when he wakes up, but right now, I expect he is just getting to bed, since we left a nice social gathering at about the same time.

Not sure why I logged on instead of crashing, actually!

In answer to your question, if you understand how air circulates around a wing, then the answer falls into your lap, I think! I'll leave you with that to ponder for now.

 

[flyTotheSky]

When you are talking about how air circulates around the wing, are you referring to Magnus effect? I was always taught that this wasn't a considerable source for lift production.

Still, I searched the tech threads and wasn't able to find much information. I know as the AOA increases the pressure differential increases and causes the forward movement towards the stagnation point, but the question still remains....

 

[tgrayson]

As we all know the CP moves along the chordline when the AOA changes. As the AOA increases, the CP moves forward and vice versa.

One thing that is confusing about the CP is the literature seems to suggest that the CP is a point that is physically special in some way, as if we could detect its position with a CP sensor. However, even if you could actually see the pressure distribution, you wouldn't be able to tell where the CP was, because it looks just like any other point on the wing. In fact at low angles of attack, it might not even be on the wing. How can this be?

In reality, the CP is something of a fiction that is useful in some circumstances, sort of like the lift vector itself. The forces on a wing are distributed all over the wing and the end aerodynamic result is a summation of all these vector quantities. These forces will produce two effects:

1) Translation (moving up, down, backwards, forwards)
2) Rotation (pitching nose down, nose up)

The translation forces become lift and drag, and we often pretend that they act at specific points on the airplane, when they really don't. However, if we choose the points carefully, our lies generate correct information.

Same thing with the rotational forces (moments). We can calculate these moments around any point on the airplane. Depending on the point, they result will sometimes be negative (nose down pitching) or positive (nose up). The CP is simply the point where the result is zero. If you were to place the CG on the CP, the aircraft would not need a horizontal tail...as long as the AOA doesn't change. ;-)

Why do we care where the CP is? We generally don't. Contrary to what you read in most places, CP isn't connected with aircraft longitudinal stability. There is a related concept called the Aerodynamic Center which is located at about the 1/4 chord point on the wing and that doesn't change with AOA. The CG must like ahead of this point for the aircraft to be stable. The CP moves all around with AOA and therefore isn't useful for stability calculations. Consider: if a CG lay ahead of the CP, an increase in AOA might move it in front of the CG, causing an uncontrollable pitch up. That won't do.

The main point behind all of the above is to communicate that the CP is primarily a mathematical concept, not a physical one, and the same concept will apply even if you want to look at lift from a Newtonian perspective. In fact, you can say that lift is caused by "Lift Demons", if you want to, and there will still be a point on the wing (or off) where the pitching moment is zero.

(Please tell me if this doesn't make any sense at all.)

 

[tgrayson]

When you are talking about how air circulates around the wing, are you referring to Magnus effect? I was always taught that this wasn't a considerable source for lift production.

Seagull is talking about circulation theory, which is how a wing generates lift. Since he brought it up, we'll let him explain.

 

[seagull]

Seagull is talking about circulation theory, which is how a wing generates lift. Since he brought it up, we'll let him explain.

That's mean, and besides, you have more time than I do right now, plus the patience for it all. Mine is all used up on real life tasks right now!

 

[fish314]

Well, I'll give a go at the circulation theory of lift production.

Ok, you already know that the air moves faster over the top of the wing than it does over the bottom. Well, once upon a time when mathematicians and physicists were trying to figure out the laws of fluid dynamics, they decided that one way to model this behaviour would be to use a vortex field, or a circulation....

Basically to imagine how this works, take out a pad and paper and draw a flow of air moving from left to right, with some constant velocity and with no wing in it. What do you get? Basically a series of straight lines representing the air moving undisturbed. You could imagine at each point on paper a little arrow pointing to the right, where the size of the arrow represented the speed of the air and the direction of the arrow represented the direction the air was moving. In fact, if you really are drawing this out on a pad of paper, add some little arrows pointing left to right on your lines.

Mathematically, what you would have just drawn is something called a vector field. And that particular vector field has a very simple mathematical formula.

Now somewhere in that vector field, draw a circulation. Basically just draw a circle and put a couple of little arrows on it going clockwise. What you've just represented is something in the vector field that is going to give a little speed boost to the stream of air where the two are pointing in the same direction and take a little speed away from the flow where the two are pointing opposite each other.

This is actually a pretty good mathematical model of a wing. Imagine your wing in the center of the circle that you just drew, and look what happened. The flow on top of the wing has the velocity of the air mass + the velocity of the circulation, so it goes a little faster than the air mass all by itself. The flow on the bottom of the wing has the velocity of the air mass - the velocity of the circulation, and that air moves a little slower. So you've just modeled the air going faster on the top than on the bottom.

This is the basics of something called Prandtl's Lifting Line theory. It's just a mathematical tool to model how the flow behaves above and below a wing. It's not super accurate, but it does provide some good predictions.

 

[flyTotheSky]

Some very great insight from people here! Thanks a lot.

I'm still a bit perplexed about what causes the movement fore and aft?

I realize that it isn't a physical point. But to contradict what I just said, there has to be some point of low pressure flowing over the stall warning vents (at a high AOA) to cause those mechanisms to go off. Is this the CP?

 

[seagull]

I think -- now let me preface this by saying that I just finished a nice little drink I'd mixed myself (how is that for a qualifier?) -- that, well, let me start out again. It seems to me that if you envision a wing in the flow, that as you increase AoA the CP will move forward for a couple of reasons. One, just the geometry relative to the free stream, but also the reduction of lift on the aft portion of the airfoil due to flow separation. The first one might be envisioned more easily with the circulation model is all I meant.

Now, I think I'll go to bed!

 

[tgrayson]

I realize that it isn't a physical point. But to contradict what I just said, there has to be some point of low pressure flowing over the stall warning vents (at a high AOA) to cause those mechanisms to go off. Is this the CP?

No, it's not the CP, for the very reason you said. There is no physical phenomenon associated with the CP and so there is no aerodynamic means to detect it. Besides, the CP will never be that forward. It is NOT a low pressure point.

<<I'm still a bit perplexed about what causes the movement fore and aft? >>

It moves fore and aft because the pressure distribution on the top and bottom of the airfoil changes with AOA, and the quantity and direction of the aerodynamic force generated by the wing depends on this distribution.

Ok, here's a challenge for you. Consider an aicraft that weights 4,000 lbs and has a wing chordline of 48 inches.

First take the wing at a low angle of attack. In this situation, there is low pressure on the top and bottom of the airfoil. You might think of the lower surface creating down lift and the upper surface create up lift. Since the lower surface isn't helping lift the airplane, the upper surface must generate enough lift for the entire airplane AND compensate for the negative lift from the lower surface. Further, the areas of suction on the top and bottom of the airfoils occur at different locations.

On the top of the airfoil, the most suction occurs near the peak camber; however, the remaining backside of the wing has a larger surface area, even though the suction is lower. Therefore, the average lift will occur some distance behind the lowest suction. Let's say 20 inches from the leading edge, and has a value of 4,400 lbs.

On the lower, the average negative lift will occur closer to the front of the airfoil, say 4 inches from the leading edge and has a value of -400 lbs.

So the total lift is 4,000, but is composed of lift from the top and negative lift from the bottom.

Can you calculate where the CP is located on this wing? This is the location around which the forces I described will produce a zero moment. Give the location in terms of inches from the leading edge.

Once you have the answer, do the same calculation at a high angle of attack. In this case, the lift on the top side of the airfoil is 2,800 lbs, but now the lower side has a positive pressure and contributes to the total lift. It provides 1,200 lbs. Both forces are located 12 inches from the leading edge. Where is the CP now?